Depending on the size the machine will take, most machines will take all folders. I have a Sizzix Texture Boutique and it works with Sizzix; Cuttlebug; QuikCuts folders. I haven't found any it won't work with except the larger 5 x 7 folders.
As Kay says - mostly yes. Each machine will just have a different sandwich of plates, folder and paper, but there are tons of instructions and youtube videos about the specific for each machine so it's easy if you get confused.